The total annual spending by tourists in a resort city is $200 million. Approxim

Question

The total annual spending by tourists in a resort city is $200 million. Approximately 80% of that revenue is again spent in the resort city, and of that amount approximately 80% is again spent in the same city, and so on. Write the geometric series that gives the total amount of spending generated by the $200 million and find the sum of the series.

www.webassign net webs udent assignment Need Help? The total annual spending tounstsin a resort city is s20o million. Approximately sow or that revenue is againspent l the resort ors and of that amount appro by mate y Bos is again spent the same ot and so on write the geometric series that ves the total amount af TOSHIBA A s D F G H J K L ALT

Explanation / Answer

In the first round of spending, 200 million dollars are spent = 2*108
In the subsequent rounds; only 80% (ratio =0.8) of it are spent and these subsequent rounds go on forever;

This geometric series can thus be represented as :
2*108 + 2*108* 0.81 + 2*108* 0.82 + 2*108* 0.83 + 2*108* 0.84 + .... so on;

The first term of this series is a = 2*108
The common ratio of this series is r= 0.8
Thus an infinite sum of Geometric progession says that the value will be = a/(1-r)
= 2*108 / (1-0.8) = 2*108 / (0.2) = 10* 108 = 109 $
Sum of series = 109 $

Thus a total of 109 $ or 1 billion dollars will be spent in that resort city;

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